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Abstract The purpose of this paper is to present the Cattaneo–Christov heat flux model for Maxwell fluid past a stretching surface where the presence of suction/injection is taken into account. The governing system of equations is reduced to the ordinary differential equations with the boundary conditions by similarity transformation. These equations are then solved numerically by two approaches, Haar wavelet quasilinearization method (HWQM) and Runge–Kutta–Gill method (RK Gill). The behavior of various pertinent parameters on velocity and temperature distributions is analyzed and discussed. Comparison of the obtained numerical results is made between both methods and with the existing numerical solutions found in the literature, and reasonable agreement is noted.

MHD viscoelastic (Walters'-B) fluid flow close to the stagnation point region along an extending plate with the changeable fluid properties' influences has been debated. Heat transfer's features are scrutinized via Cattaneo–Christov (CC) theory. The mathematical model for the physical problem is tackled numerically via Chebyshev pseudospectral (CPS) technique. The existing outcomes are supported by recent research and have acquired a suitable agreement. The numerical outcomes reveal that temperature fields are more pronounced for Fourier's law case. Further, the opposite behavior is noticed with the heat transfer rate. Higher values of the conjugate parameter result in an increment of the heat transfer rate and temperature field. Fluid flow's features, as well as physical quantities, are substantially varied via variable fluid properties. [ABSTRACT FROM AUTHOR]

This study explores the heat and mass transfer of Casson nanofluid flow containing gyrotactic microorganisms past a swirling cylinder. Fluid flow is generated owing to the torsional movement of the cylinder. An analysis is performed in the presence of gyrotactic microorganisms. The effects of chemical reaction, magnetohydrodynamics, heat generation/absorption, and zero mass flux condition are also considered. The Cattaneo–Christov heat flux model is initiated instead of conventional Fourier heat flux. Apposite transformations are betrothed to attain the coupled system of equations. The numerical solution is developed from the novel mathematical model via bvp4c function utilizing MATLAB software. Numerous graphs and tables are established to portray the inspiration of embroiled parameters on the flow distributions. To corroborate the presented results; a comparison to an already done published paper is also made. An excellent synchronization between the two results is obtained thus endorsing the presented model. Also, form the graphical structures and numerically erected tables, it is professed that concentration of the fluid is lessened owing to an upsurge in values of Reynolds number and Brownian motion parameter. Furthermore, diminishing density of microorganism is perceived for mounting estimates of bioconvection Péclet number. [ABSTRACT FROM AUTHOR]

In this article, we explore the three-dimensional boundary-layer flow over an exponentially stretching surface in two parallel ways. Constitutive equations of a second-grade fluid are used. Instead of classical Fourier's law, Cattaneo–Christov heat flux model is employed for the formulation of the energy equation. This model can predict the effects of thermal relaxation time on the boundary layer. The resulting partial differential equations are reduced into ordinary differential equations by similarity transformations. Homotopy Analysis Method (HAM) is employed to solve the non-linear problem. Physical impact of emerging parameters on the momentum and thermal boundary-layer thickness are studied. [ABSTRACT FROM AUTHOR]

The purpose of this research is to scrutinize the stagnation point flow of chemically reacting Powell–Eyring nanofluid past an inclined cylinder using the impact of activation energy with Cattaneo–Christov heat flux. Flow formulation is developed by considering the impact of nonlinear thermal radiation, binary chemical reaction, non-Fourier heat flux and the Buongiorno nanofluid model. Proper transforms yield highly nonlinear differential systems, which are solved using shooting procedure with the fourth-order R–K (Runge–Kutta) method. Comparative reviews between the formerly published literature and the current data are made for specific cases, which are inspected to be in a tremendous agreement. The narrative reviews show that the current research problem has not premeditated so far. Effectiveness of innumerable parameters is publicized graphically on velocity, temperature and concentration curves cases of various angles 0° horizontal cylinder, 45° inclined cylinder and 90° vertical cylinder. It is manifested that fluid velocity promotes with the larger values of velocity ratio. It is also noticed that concentration declines when destructive chemical reaction enhances, whilst the antithesis direction is noticed in the condition of the generative chemical reaction. Furthermore, the stream lines are closer to the cylindrical wall when α = 90° and the stream lines are far away to the cylindrical wall when α = 90°. [ABSTRACT FROM AUTHOR]

Nanofluids have the ability to flow smoothly in micro-cavities in addition with scattering of the nanoparticles. Because of the good convection between nanoparticles and the base fluid, nanofluids can achieve a good thermal conductivity. The main advantages of adding nanosize particles with base fluid are to improve the ability of storing heat, effective surface area, heat transmission, collisions and interaction among the nanoparticles. The main aim of this research work is to examine the steady and incompressible nanofluid flow between parallel rotating plates. Viscose and joule dissipation effects are taken into account. To our knowledge, impact of electrical MHD and Hall effect with Cattaneo–Christov heat flux on the squeezing 3-D flow nanofluid between parallel rotating plates are not examined yet. Heat in the form of Cattaneo–Christov heat flux is applied. We used similarity transformations to transform the primary equations to a system of ordinary differential equations (ODEs). These ODEs are then solved through the standard procedure of homotopy analysis technique. The skin friction and Nusselt number are numerically tabulated under the influence of some focused parameters. The effects produced by different parameters on the velocity (components) and temperature profiles are graphically depicted and explained in a bit detail. [ABSTRACT FROM AUTHOR]

The present work focused here is a mixed convective MHD flow of cross fluid in the presence of heat generation/absorption and variable thermal conductivity over a bidirectional stretchable sheet. To elaborate the mechanism of heat transfer is analyzed in view of non-Fourier heat flux based upon Cattaneo–Christov theory. The influence of a simple isothermal model of homogeneous–heterogeneous reactions is further used for solute concentration. As a result, the relevant Buongiorno fluid model is utilized in mathematical modeling and then it is simplified through lubrication technique. By using appropriate transformations, the raised PDEs initially converted to ODEs. Convergent solutions of ODEs are obtained by the implementation of the numerical procedure bvp4c technique. However, the velocity, temperature and concentration profiles have been sketched by distinct physical flow parameter. Drag coefficients and heat transport are also computed numerically. Our results reveal that temperature profile has an inverse relation between the relaxation parameter and variable thermal conductivity. [ABSTRACT FROM AUTHOR]

The purpose of this study is to investigate the impact of thermal relaxation time on the mixed convection flow of non-Newtonian micropolar fluid over a continuously stretching sheet of variable thickness in the presence of transverse magnetic field. An innovative and modified form of Fourier's law, namely, Cattaneo-Christov heat flux is employed in the energy equation to study the characteristics of thermal relaxation time. The governing equations are transformed into ODE, using similarity transformations. Fourth order Runge-Kutta numerical method is used to solve these equations. The effects of relevant parameters such as a micro-rotation parameter, magnetic parameter, thermal relaxation parameter, Prandtl number, surface thickness parameter, and mixed convection parameter, on the physical quantities are graphically presented. Results illustrate that fluid temperature enhances with the rise of thermal relaxation parameter, but it reduces with an increase in micro-rotation parameter. The skin friction decreases with a rise in micro-rotation and micro-element parameters. However, variation in the rate of heat transfer is quite significant for small values of thermal relaxation parameter. [ABSTRACT FROM AUTHOR]

With an objective to unfold the flow and heat transfer characteristics of carbon nanotubes between two stretchable coaxial rotating disks, the present investigation has been carried out. The behavior of single- and multi-walled carbon nanotubes (SWCNTs and MWCNTs) taking water as the base fluid is analyzed. To formulate the energy equation, we have incorporated Cattaneo–Christov heat flux model. Consideration of such kind of model accounts the contribution by thermal relaxation. von Karman transformation has been implemented in order to reconstruct the governing partial differential equations into a system of ordinary differential equations. Employing optimal homotopy analysis method series solutions are obtained. Error analysis has also been performed and presented in tabular form. The physical clarifications for the behavior of fluid velocity, temperature, skin friction coefficient and Nusselt number are well demonstrated with the help of graphs and contour plots. One of the major outcomes of the present study signifies that water-based SWCNTs have a tendency to cause less drag and higher rate of heat transfer as compared to water-based MWCNTs. This investigation finds numerous applications in different mechanisms of thermal conversion for nuclear propulsion and spacecraft. [ABSTRACT FROM AUTHOR]

In this article, the boundary layer flow of a viscous nanofluid induced by an exponentially stretching surface embedded in a permeable medium with the Cattaneo–Christov heat flux model (CCHFM) is scrutinized. We took three distinct kinds of nanoparticles, such as alumina (Al2O3), titania (TiO2) and copper (Cu) with pure water as the base fluid. The features of the heat transfer mechanism, as well as the influence of the relaxation parameter on the present viscous nanofluid flow are discussed here thoroughly. The thermal stratification is taken in this phenomenon. First of all, the problem is simplified mathematically by utilizing feasible similarity transformations and then solved analytically through the OHAM (optimal homotopy analysis method) to get accurate analytical solutions. The change in temperature distribution and axial velocity for the selected values of the specific parameters has been graphically portrayed in figures. An important fact is observed when the thermal relaxation parameter (TRP) is increased progressively. Graphically, it is found that an intensification in this parameter results in the exhaustion of the fluid temperature together with an enhancement in the heat transfer rate. A comparative discussion is also done over the Fourier's law and Cattaneo–Christov model of heat. [ABSTRACT FROM AUTHOR]

The flow of fluid over a surface that is being stretched has numerous important potential uses, such as polymer extrusion, coating, etc. The objective of this study is to investigate the characteristics of flow attributes (velocity, temperature, skin friction coefficient, and local Nusselt number) under specific conditions, when a quadratic convective flow of tangent hyperbolic fluid is applied over a non-flat stretching sheet. In this case, the transfer of heat is simulated by employing a modified version of Fourier's law and complemented with quadratic thermal radiation. The resolution of the governing partial differential equations is achieved by initially transforming them into ordinary differential equations and subsequently employing the Legendre wavelet collocation technique (LWCT). Moreover, β − cut technique of fuzzy numbers are utilized in ODEs to obtained FDEs (Fuzzy differential equation) and FDEs are solved by triangular fuzzy number (TFN). The numerical computation involves the treatment of We and Rd as fuzzy numbers. The findings suggest that the fluid temperature drops when the relaxation parameter is raised. Moreover, Fuzzy temperature profile decreases with increasing A 1 , A 2 and fuzzy parameter β. The current code demonstrates a high degree of concurrence when subjected to numerical validation in comparison to prior research. [ABSTRACT FROM AUTHOR]

PTSCs (parabolic trough solar collectors) are widely employed in solar-thermal applications to attain high temperatures. The purpose of this study is to determine how much entropy is created when Powell-Eyring nanofluid (P-ENF) flows across porous media on a horizontal plane under thermal jump circumstances. The flow in PTSC was generated by nonlinear surface stretching, thermal radiation, and Cattaneo-Christov heat flux, which was utilized to compute heat flux in the thermal boundary layer. Using a similarity transformation approach, partial differential equations were converted into ordinary differential equations with boundary constraints. Then, the boundary restrictions and partial differential equations were merged to form a single set of nonlinear ordinary differential equations. To obtain approximate solutions to ordinary differential equations, the Keller-Box approach is utilized. Nanofluids derived from silver- and copper-based engine oil (EO) has been employed as working fluids. The researchers observed that changing the permeability parameter reduced the Nusselt number while increasing the skin frictional coefficient. Total entropy variation was also calculated using the Brinkman number for flow rates with Reynolds number and viscosity changes. The key result is that thermal efficiency is inversely proportional to particular entropy production. For example, using Cu-EO nanofluid instead of Ag-EO nanofluid increased the heat transport rate efficiency to 15–36%.

The problem of micropolar fluid flow over a nonlinear stretching convective vertical surface in the presence of Lorentz force and viscous dissipation is investigated. Due to the nature of heat transfer in the flow past vertical surface, Cattaneo-Christov heat flux model effect is properly accommodated in the energy equation. The governing partial differential equations for the flow and heat transfer are converted into a set of ordinary differential equations by employing the acceptable similarity transformations. Runge-Kutta and Newton’s methods are utilized to resolve the altered governing nonlinear equations. Obtained numerical results are compared with the available literature and found to be an excellent agreement. The impacts of dimensionless governing flow pertinent parameters on velocity, micropolar velocity and temperature profiles are presented graphically for two cases (linear and nonlinear) and analyzed in detail. Further, the variations of skin friction coefficient and local Nusselt number are reported with the aid of plots for the sundry flow parameters. The temperature and the related boundary enhances enhances with the boosting values of M. It is found that fluid temperature declines for larger thermal relaxation parameter. Also, it is revealed that the Nusselt number declines for the hike values of Bi.

The knowledge of heat transfer of MHD flows across a stretched surface plays a crucial role in transportation, heat exchangers, fibre coating, magnetic drug treatment, etc. The present research article delivers a numerical examination of 2D magnetohydrodynamic nonlinear radiative flow of micropolar fluid towards a stretching surface. The fluid motion is steady and laminar. The impacts of chemical reaction, cross-diffusion and thermal and solutal Biot numbers are deemed. Combined influence of heat and mass transfer attributes is investigated. For effective heat transfer, Cattaneo–Christov heat flux term is added to the energy equation. The appropriate transmutations are adopted for rehabilitating the flow governing PDEs into dimensionless ordinary ones. Further, these ODEs are resolved by R.K.F-4 with a shooting system. The graphs are plotted to picture the flow fields for the flow regulating parameters. The friction factor, couple stress and mass and thermal transport rates are presented for the flow relevant variables. From the results, we spotted that there are an enhancement in velocity but a decrement in temperature and concentration fields with the swelling in the values of primary slip parameter. Also the temperature and concentration fields are enhanced with the boosting values of Dufour and Soret numbers, respectively. [ABSTRACT FROM AUTHOR]

A theoretical model is drafted to inspect the hydromagnetic flow of carbon nanotubes (CNT's) suspended in a Maxwell nanofluid by means of activation energy with binary chemical reaction over a stretching sheet. Modified Arrhenius function is measured instead of the energy activation. Heat transport phenomena are explored in energy expression through a nonlinear thermal radiation and viscous dissipation, which is incorporated with a novel theory specifically Cattaneo–Christov model of heat diffusion—a sophisticated form of Fourier's heat flux formula. The flow analysis is reported in attendance of convective slip and suction. Two different kinds of CNT's (i.e. single and multiple walls) are consistently dispersed in the base fluid (engine oil) to illustrate the fine points of the flow. The governing system of mathematical expressions for the locally similar flow is tackled numerically by Runge–Kutta-based MATLAB bvp4c package. The procured solutions are drawn for different values of pertinent parameters of interest. The temperature of the fluid escalates with the nonlinear thermal radiation. Activation energy boosts up the concentration, and a negative trend is observed for rate of chemical reaction. [ABSTRACT FROM AUTHOR]

The present article investigates the effect of second-order slip, chemical reaction and Soret and Dufour effects on MHD convective flow of an Oldroyd-B liquid toward a stretchy surface. Analysis of thermal relaxation time is made by using Cattaneo-Christov heat flux model. The effects of radiation and convective heating are also taken into account. The ordinary differential equations are retrieved by the help of suitable transformations of governing equations. The analytical solutions are observed by homotopy progress. The velocity, concentration and temperature field are analyzed for various pertinent parameters involved in the study. The graphical results of physical quantities of interest such as skin friction, local Nusselt number and local Sherwood number are presented. A comparative study with existing result indicates excellent agreement. [ABSTRACT FROM AUTHOR]

The amazing features of carbon nanotubes (CNTs), such as lightweight, high thermal conductivity, good electrical conductivity, mechanical and chemical stability, and physiochemical compatibility, make them highly desirous materials for use in the electrochemical gadgets. Having such magnificent characteristics of carbon nanotubes in mind, our aim in this study is to examine the time-dependent squeezing nanofluid flow of water-based single- and multi-walled carbon nanotubes (SWNTs and MWNTs) in attendance of homogenous-heterogeneous (h-h) reactions between two parallel disks. The present study further comprises the impacts of magnetohydrodynamics (MHD) and Cattaneo-Christov (C-C) heat flux. Numerical solution of ordinary differential equations after engaging apposite transformations is computed. Concentration, temperature, velocity, local Nusselt number, and skin friction coefficient are addressed. Presented analysis reveals that skin friction and Nusselt number show opposite behavior for squeezing parameter Sq for both water-based SWNTs and MWNTs. Furthermore, the velocity field grows for mass transfer parameter. An outstanding consensus is achieved when our presented results are compared with an already studied problem in limiting case. Thus, dependable results are being presented. [ABSTRACT FROM AUTHOR]

The current study aims to explore the magnetic field on a spinning disk with the hybrid nanofluid flow and Cattaneo-Christov heat theory in the existence of nonlinear thermal radiation incorporating Ag and MnZnFe2O4 nanoparticles. Because silver may increase the thermal characteristics of the base material, it has a wide variety of industrial, pharmaceutical, power generation, and heating and cooling applications. The thermal properties of a hybrid nanofluid were to be found by exploring the aspect of nanomaterials on heat transfer and fluid flow. The principal partial differential equations are converted into ordinary differential equations using appropriate similarity treatments. With the aid of the shooting strategy, higher-order ordinary differential equations are converted to first-order ordinary differential equations. To present the numerical data and graphical results of the flow parameters, the built-in solver Bvp4c in the computational tool MATLAB is used. Several plots are also used to investigate the upshot of physical parameters on the graphically depicted profiles, such as the suction and injection parameter, magnetic parameter, Prandtl number, temperature ratio parameter, thermal radiation parameter, thermal relaxation parameter, and volume friction nanoparticles. For the magnetic parameter, both velocity profiles dropped, but the heat profile increased. When the temperature ratio and heat source-sink parameters were increased while the Prandtl number was decreased, the heat field increased. [ABSTRACT FROM AUTHOR]

Heat and mass flux conditions on magnetohydrodynamic unsteady Eyring-Powell dusty nanofluid over a sheet is addressed. The combined effect of Brownian motion and thermophoresis in nanofluid modeling are retained. The Cattaneo-Christov heat flux model is imposed. A set of similarity variables are utilized to form ordinary differential system from the prevailing partial differential equations. The problem of ordinary differential system (ODS) is analyzed numerically through Runge-Kutta based shooting method. Graphical results of pertinent parameters on the velocity, temperature and nanoparticle concentration are studied. Skin friction coefficient, local Nusselt and Sherwood number are also addressed with help of graphs and also validated the present solutions with already existing solutions in the form of table. It is found that the thermal relaxation parameter improves the heat transfer rate and minimizes the mass transfer rate. The heat transfer rate is higher in prescribed heat flux (PHF) case when compared with prescribed wall temperature (PWT) case.

An analysis is introduced to investigate the salient features of nonlinear convective flow of thixotropic fluid in the version of Cattaneo-Christov heat flux theory. The stagnation point flow is present. The flow phenomenon is by an impermeable stretching sheet. The energy expression is modeled through the theory of Cattaneo-Christov heat flux. Characteristics of heat transfer phenomenon are described within the frame of variable thermal conductivity. Suitable variables reduced to the nonlinear partial differential expressions to the ordinary differential expressions. Series solutions of resulting systems are acquired within the frame of homotopy theory. Convergence analysis is achieved and suitable values are determined by capturing the so-called ℏ−curves. Graphical results for velocity and temperature are displayed and argued for sundry physical variables. Expression of skin friction coefficient is calculated through numerical values. Higher values of mixed convection parameter, Prandtl number, and thermal relaxation time lead to decay the temperature and layer thickness. [ABSTRACT FROM AUTHOR]

Abstract This is a speculative investigation of the magnetohydrodynamic flow of Eyring-Powell liquid under suspension of nano-particles and dust. A simulation is executed by fraternization of Ferrous oxide (Fe 3 O 4) and aluminum oxide (Al 2 O 3) nanoparticles in Eyring-Powell dusty fluid. Dispersion of ferrous oxide (Fe 3 O 4) and aluminum oxide (Al 2 O 3) nano-particles in dusty fluid have applications in heat exchanger system, biocompatibility, biosensors, nuclear reactor heating process, detection and cancer treatment, in monitoring stem cells differentiation etc. Ferrous oxide (Fe 3 O 4) and aluminum oxide (Al 2 O 3) mixtures are substantially useful in optimizing the heat transport occurrences. Implementation of similarity variables leads to the systems of ordinary differential expressions. These nonlinear systems of ODEs are tackled with the use of Runge-Kutta-Fehlberg Scheme (RKFS). The analysis of dimensionless temperature and velocity fields is given via plots. The numerical benchmarks of friction-factors and heat transport rate are for different constraints are given and examined. Obtained results are matched with previously published material and noted to be satisfactory. This model expresses that the rate of heat transportation is more in aluminum oxide nanofluid compared to ferrous oxide nanofluid with existing of viscous variation parameter. The presence of thermal and momentum slips correspond the enhancement in local Nusselt number in case of ferrous oxide nanoparticles when compared to aluminum oxide nanoparticles. Graphical Abstract Unlabelled Image Highlights • Magnetohydrodynamic Eyring-Powell fluid in a suspension of dust and nanoparticles is considered. • A simulation is executed by fraternization of nanoparticles into dusty liquid. • The numerical solutions are obtained through Runge-Kutta Fehlberg scheme. • The computational results for of velocity and temperature are presented. [ABSTRACT FROM AUTHOR]

The main purpose of this research is to evaluate the impact of Darcy–Forchheimer flow in an incompressible third‐grade liquid through Cattaneo–Christov heat flux approach. The Cattaneo–Christov heat flux theory is adopted to govern the mathematical expression of energy, which involves the heat flux relaxation time chracteristics. Time‐dependent thermal conductivity is accounted. The steady problem is reduced to ordinary differential equations via suitable transformation. Numerical solutions for the resulting flow expressions have been computed with the help of Euler's explicit technique. Impact of influential variables on the velocity, temperature and skin‐friction coefficient have been demonstrated and discussed through graphs. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A Comprehensive study on laminar, magnetohydrodynamic (MHD) boundary layer flow of nanofluid (water + Silver, water + Graphene) embedded with conducting micrometer sized dust particles over a stretching cylinder with the incorporation of Cattaneo-Christov heat flux model is conducted. Appropriate similarity variables are employed to the flow governing equations and the resulting ordinary differential equations are solved by employing Runge-Kutta-Fehlberg method. The results for varied controlling parameters for both dusty nano fluid and dust phase are shown through graphs, table and discussed in detail. Authentication of the obtained results is provided by comparing with published results. Results indicate that Graphene + water dusty nanofluid shows better heat transfer performance compared with Silver + water dusty nanofluid. Improvement in thermal relaxation boosts temperature distribution in both fluid and dust phase. [ABSTRACT FROM AUTHOR]

This is a theoretical study of unsteady nonlinear convection on magnetohydrodynamic fluid in a suspension of dust and graphene nanoparticles. For boosting the heat transport phenomena we consider the Cattaneo-Christov heat flux and thermal radiation. Dispersal of graphene nanoparticles in dusty fluids finds applications in biocompatibility, bio-imaging, biosensors, detection and cancer treatment, in monitoring stem cells differentiation etc. Initially the simulation is performed by amalgamation of dust (micron size) and nanoparticles into base fluid. Primarily existing partial differential system (PDEs) is changed to ordinary differential system (ODEs) with the support of usual similarity transformations. Consequently, the highly nonlinear ODEs are solved numerically through Runge-Kutta and Shooting method. The computational results for Non-dimensional temperature and velocity profiles are offered through graphs ( ϕ = 0 and ϕ = 0.05 ) cases. Additionally, the numerical values of friction factor and heat transfer rate are tabulated numerically for various physical parameters obtained. We also validated the current outcomes with previously available study and found to be extremely acceptable. From this study we conclude that in the presence of nanofluid heat transfer rate and temperature distribution is higher compared to micro fluid. [ABSTRACT FROM AUTHOR]

A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic (MHD) Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips (diffusion, thermal, and momentum slips) are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that the velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena. [ABSTRACT FROM AUTHOR]

In this article, we investigate the convective heat transfer of the two-dimensional unsteady squeezing flow past a Riga plate. To examine the heat transfer, Cattaneo-Christov heat flux model is used. Influence of entropy generation on heat transfer has been investigated numerically. With the help of suitable similarity transformation, the governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs). The obtained system of non-linear ordinary differential equations subject to the convective boundary conditions is solved by the shooting method using the computational software MATLAB. To strengthen the reliability of the results obtained by the shooting method, the MATLAB built-in function bvp4c has been used. The graphs show the effect of different physical parameters for velocity, temperature, concentration and tables are presented to observe the behaviour of skin friction and sherwood number under the influence of certain physical parameters. It is observed that for increasing values of thermal relaxation parameter, the temperature profile increases and an opposite behaviour is shown for the concentration profile. Moreover, with an increase in the Brinkman number, the entropy generation increases. [ABSTRACT FROM AUTHOR]

A theoretical model on carbon nanotube-based upper convective Maxwell nanofluid flow with thermal and velocity slip boundary conditions is thoroughly presented here. To formulate the viscoelastic relaxation framework on boundary layer flow uniquely, Cattaneo-Christov heat flux model is employed in the momentum equation. The dominating equations and boundary conditions are turned into system of ordinary boundary value problem by using proper transformations, and hence, the similarity solutions are gained numerically by applying Runge-Kutta fourth-order method with shooting practice. The impacts of the governing parameters upon the flow and temperature are represented in tabular as well as in graphical form and discussed in detail. The findings elucidate that both the velocity and temperature are inverse functions of thermal relaxation time for single-walled and multi-walled carbon nanotube-based nanofluids. Fluid relaxation parameter is positively correlated with skin friction and rate of heat transport for both types of nanofluids, but the temperature slip makes a contrary with the same. [ABSTRACT FROM AUTHOR]

In the present article, the problem of boundary layer flow of MHD electrically conducting fluid past a cone and a wedge with non-uniform heat source/sink along with Cattaneo-Christov heat flux is investigated numerically. At first, the flow equations are converted into ODE via appropriate self similarity transforms and the resulting equations are solved with the assistance of R.-K. and Newton’s methods. The influence of several dimensionless parameters on velocity and temperature fields in addition to the friction factor and reduced heat transfer coefficient has been examined with the support of graphs and numerical values. The heat transfer phenomenon in the flow caused by the cone is excessive when compared to the wedge flow. Also, the thermal and momentum boundary layers are not the same for the flow over a cone and wedge. [ABSTRACT FROM AUTHOR]

In this communication we utilized a modified Fourier approach featuring thermal relaxation effect in nonlinear convective flow by a vertical exponentially stretchable surface. Temperature-dependent thermal conductivity describes the heat transfer process. Thixotropic liquid is modeled. Convergent local similar solutions by homotopic approach are obtained. Graphical results for emerging parameters of interest are analyzed. Skin friction is calculated and interpreted. Consideration of larger local buoyancy and nonlinear convection parameters yields an enhancement in velocity distribution. Temperature and thermal layer thickness are reduced for larger thermal relaxation factor. [ABSTRACT FROM AUTHOR]

In this article, the boundary layer flow of a viscous nanofluid induced by an exponentially stretching surface embedded in a permeable medium with the Cattaneo−Christov heat flux model (CCHFM) is scrutinized. We took three distinct kinds of nanoparticles, such as alumina (Al2O3), titania (TiO2) and copper (Cu) with pure water as the base fluid. The features of the heat transfer mechanism, as well as the influence of the relaxation parameter on the present viscous nanofluid flow are discussed here thoroughly. The thermal stratification is taken in this phenomenon. First of all, the problem is simplified mathematically by utilizing feasible similarity transformations and then solved analytically through the OHAM (optimal homotopy analysis method) to get accurate analytical solutions. The change in temperature distribution and axial velocity for the selected values of the specific parameters has been graphically portrayed in figures. An important fact is observed when the thermal relaxation parameter (TRP) is increased progressively. Graphically, it is found that an intensification in this parameter results in the exhaustion of the fluid temperature together with an enhancement in the heat transfer rate. A comparative discussion is also done over the Fourier’s law and Cattaneo−Christov model of heat.

The knowledge of heat and mass transfer of MHD flows over different geometries is very important for heat exchangers design, transpiration, fiber coating, etc. With this initiation, a mathematical model is proposed to investigate the two-dimensional flow, heat and mass transfer of magnetohydrodynamic flow over three different geometries (vertical cone, vertical wedge, and a vertical plate). Cattaneo-Christov heat flux with external magnetic field, thermophoresis and Brownian movement effect are introduced in the model. Runge-Kutta and Newton’s methods are employed to solve the altered governing nonlinear equations. The influences of the parameters of concern on the common profiles (velocity, temperature, and concentration) are conversed (in three cases). By viewing the same parameters, skin friction coefficient, heat and mass transfer rates are discussed with the assistance of tables. It is discovered that the momentum and thermal boundary layers are non-uniform for the MHD flow over three geometries (vertical cone, wedge, and a plate). Thermal and solutal Grashof numbers regulate the temperature and concentration fields. The heat and mass transfer rates of the flow over a cone are highly influenced by the thermal relaxation parameter. [ABSTRACT FROM AUTHOR]

The problem of micropolar fluid flow over a nonlinear stretching convective vertical surface in the presence of Lorentz force and viscous dissipation is investigated. Due to the nature of heat transfer in the flow past vertical surface, Cattaneo-Christov heat flux model effect is properly accommodated in the energy equation. The governing partial differential equations for the flow and heat transfer are converted into a set of ordinary differential equations by employing the acceptable similarity transformations. Runge-Kutta and Newton's methods are utilized to resolve the altered governing nonlinear equations. Obtained numerical results are compared with the available literature and found to be an excellent agreement. The impacts of dimensionless governing flow pertinent parameters on velocity, micropolar velocity and temperature profiles are presented graphically for two cases (linear and nonlinear) and analyzed in detail. Further, the variations of skin friction coefficient and local Nusselt number are reported with the aid of plots for the sundry flow parameters. The temperature and the related boundary enhances enhances with the boosting values of M. It is found that fluid temperature declines for larger thermal relaxation parameter. Also, it is revealed that the Nusselt number declines for the hike values of Bi. [ABSTRACT FROM AUTHOR]

This communication addresses unsteady squeezing flow of second grade liquid. NonFourier heat flux model is implemented to discuss heat transfer features subject to heat generation/absorption. Homogeneous-heterogeneous reactions are addressed. Firstly, the problems are nondimensionalized by suitable variables and then solutions for strong nonlinear systems are presented. Convergence region is particularly determined for obtained solutions. Statistical declaration and probable error for drag force are computed. Velocity is found to decay for larger estimation of fluid parameter while thermal and concentration fields are enhanced for higher heat generation and squeezing parameters. Unsteady two-dimensional squeezing flow of an incompressible second grade liquid is considered. Plate at y = 0 is stretched with while plate at is squeezed with V h. At t = 0 and we obtained and h( t) = 0 respectively. Note that giving an inconsistency to the present flow configuration. Therefore we can't take t = 1/ c. [ABSTRACT FROM AUTHOR]

This paper addresses the squeezed flow of third grade fluid between two parallel disks. Heat transfer in present flow is characterized by Cattaneo-Christov theory. Thermal relaxation time effects on the boundary layer is examined. Suitable transformations are invoked for a system of ordinary differential equations. Convergent series solutions are thus obtained using homotopic approach. Influences of different parameters on the velocity and temperature profile are discussed. [ABSTRACT FROM AUTHOR]

Two-dimensional squeezing flow of second grade fluid between two parallel plates is addressed. The lower plate is stretched while the upper plate is either moving away or towards the lower one. Temperature-dependent thermal conductivity is considered. Further, heat source/sink is present. Unlike the classical situation, the heat flux by Cattaneo-Christov theory is adopted instead of Fourier's heat conduction law. Homotopic convergent solutions of velocity and temperature are developed and analyzed. Reduction in the thermal layer thickness is observed for Cattaneo-Christov heat flux model when compared with that of Fourier's law of heat conduction. It is observed that velocity profile is enhanced by increasing the squeezing parameter. Also, a positive squeezing parameter enhances the thermal field due to a higher squeezing force applied on the fluid. [ABSTRACT FROM AUTHOR]

The role of the Cattaneo-Christov heat flux theory in the two-dimensional laminar flow of the Jeffrey liquid is discussed with a vertical sheet. The salient feature in the energy equation is accounted due to the implementation of the Cattaneo-Christov heat flux. A liquid with variable thermal conductivity is considered in the Darcy-Forchheimer porous space. The mathematical expressions of momentum and energy are coupled due to the presence of mixed convection. A highly nonlinear coupled system of equations is tackled with the homotopic algorithm. The convergence of the homotopy expressions is calculated graphically and numerically. The solutions of the velocity and temperature are expressed for various values of the Deborah number, the ratio of the relaxation time to the retardation time, the porosity parameter, the mixed convective parameter, the Darcy-Forchheimer parameter, and the conductivity parameter. The results show that the velocity and temperature are higher in Fourier's law of heat conduction cases in comparison with the Cattaneo-Christov heat flux model. [ABSTRACT FROM AUTHOR]

The present article addresses the stagnation point flow of Jeffrey liquid towards a stretching cylinder. Heat transfer is analyzed in view of non-Fourier heat flux and thermal stratification. Expression of heat flux is based upon Cattaneo–Christov theory. Cattaneo–Christov heat flux model is utilized for the development of energy equation. Such consideration accounts the contribution by thermal relaxation. The series solutions for resulting flow and heat transfer problems have been computed. Interval of convergence for the obtained series solutions is explicitly determined. Physical quantities of interest have been examined for the influential variables entering into the problems. It is observed that velocity profile shows decreasing behavior for larger Deborah number. Further that temperature distribution decreases for larger values of thermally stratification and thermal relaxation parameters. [ABSTRACT FROM AUTHOR]

• Hybrid nanomaterial saturates through Darcy-Forchheimer porous medium placed between two infinite parallel plates is examined. • Heat transfer analysis is explored via Cattaneo-Christov heat flux model. • Flow is originated by squeezing of the upper plate. • Entropy and bejan number is also reported. • Shooting technique is adopted for solution purpose. Hybrid nanofluid bounded between two infinite parallel surfaces in presence of D-F (Darcy-Forchheimer) porous medium is explored in this analysis. Heat transport is explored by C-C (Cattaneo-Christov) heat flux and thermal radiation. Flow is originated due to squeezing of upper and stretching infinite surfaces. Entropy and Bejan number are part of this study. Lower surface is subject to convective boundary condition. Mathematical modeling of flow field is done under aforementioned assumptions. By transformation technique, PDEs (flow and heat transport expressions) are changed into ODEs. Solutions are obtained via ND-solve (shooting technique). Quantities of our interests (flow, entropy, velocity, Bejan number, skin friction) are evaluated under involved variables. Velocity of both hybrid nanomaterial and nanofluid boosts against higher squeezing and porosity parameters and Forchheimer number. Dominated behavior of velocity in case of hybrid nanomaterial is observed when compared with nanofluid. Fluid temperature intensifies by squeezing parameter and Eckert number while reduction occurs for radiation parameter. Variation in temperature is more for hybrid nanomaterial. Entropy production rate reduces for higher squeezing parameter while it increases through porosity parameter. Bejan number is an increasing function of squeezing parameter while it reduced for porosity parameter. Skin friction is controlled by squeezing parameter and Forchheimer number. [ABSTRACT FROM AUTHOR]

The knowledge of heat transfer in MHD nanofluid flows over different geometries is very important for heat exchangers design, transpiration, fiber coating, etc. Recent days, heat transfer of non-Newtonian nanofluids plays a major role in manufacturing processes due to its shear thinning and thickening properties. Naturally, magnetite (Fe 3 O 4 ) nanoparticles move randomly within the base fluid. By applying the transverse magnetic field, the motion of those nanoparticles becomes uniform. This phenomenon is very useful in heat transfer processes. With this initiation, a mathematical model is developed to investigate the heat transfer behaviour of electrically conducting MHD flow of a Casson nanofluid over a cone, wedge and a plate. We consider a Cattaneo-Christov heat flux model with variable source/sink and nonlinear radiation effects. We also considered water as the base fluid suspended with magnetite nanoparticles. R-K-Felhberg-integration scheme is employed to resolve the altered governing nonlinear equations. Impacts of governing parameters on common profiles (temperature and velocity) are conversed (in three cases). By viewing the same parameters, the friction factor coefficient and heat transfer rate are discussed with the assistance of tables. It is found that the boundary layers (thermal and flow) over three geometries (cone, wedge and a plate) are not uniform. It is also found that the thermal relaxation parameter effectively enhances the heat local Nusselt number and the heat transfer performance is high in the flow over a wedge when compared with the flows over a cone and plate. [ABSTRACT FROM AUTHOR]

The current investigation presents Darcy-Forchheimer flow of viscous fluid caused by a curved stretching sheet. Flow for porous space is characterized by Darcy-Forchheimer relation. Concept of homogeneous and heterogeneous reactions is also utilized. Heat transfer for Cattaneo–Christov theory characterizing the feature of thermal relaxation is incorporated. Nonlinear differential systems are derived. Shooting algorithm is employed to construct the solutions for the resulting nonlinear system. The characteristics of various sundry parameters are studied and discussed. Skin friction coefficient and heat transfer rate are numerically described. [ABSTRACT FROM AUTHOR]

An analysis is performed to investigate flow between two stretchable rotating disks. Thermal equation is constructed by Cattaneo-Christov heat flux theory. Porous medium is also taken into account. The nonlinear partial differential equations are first converted to ordinary differential equations and then computed for the convergent series solutions. Discussion about impact of dimensionless parameters on velocities, temperature and skin friction coefficient is given. It is observed that the radial velocity at upper disk enhances for larger values of ratio of corresponding stretching rate to angular velocity. Velocity in y -direction decays with an increase in rotational parameter. Magnitude of temperature profile decays for larger Prandtl number and thermal relaxation parameter. [ABSTRACT FROM AUTHOR]